The man, whose identity and condition have not been released, was taken to a hospital for treatment.
"Members of the uniformed Secret Service responded and administered first aid to the individual until D.C. fire and EMS arrived," said Secret Service public relations spokesman Jonathan Cherry. "The individual has been transported to the burn unit at Medstar at the Washington Hospital Center. An investigation is currently under way."
The investigation is being conducted by U.S. Park Police, whose jurisdiction includes the property directly outside the fence surrounding the White House.
President Bush went about his regular schedule during and after the incident, said White House spokesman Trent Duffy.
One witness said the man approached a security checkpoint building at the northwest gate of the White House and showed a writing pad with the word "urgent" written on it. When a uniformed Secret Service guard asked if he could help him, the man began walking along the fence toward the guard.
Another witness near the scene heard the unidentified man yelling in Arabic, "God is great," several times. And several witnesses said a bag the man was carrying started burning, pouring out thick black smoke that enveloped him.
The man appeared to fall face forward on the ground in front of the gate security building, the witnesses said, and uniformed Secret Service agents rushed to put out the flames with a fire extinguisher.
The section of Pennsylvania Avenue in front of the White House was cordoned off. Secret Service agents evacuated the immediate area in front of the White House, including the North Lawn area used by television organizations and other journalists, while initial examinations of the man and his bag were conducted.